METHOD FOR THE RAPID ANALYSIS OF A MIXTURE OF A NUMBER OF SUBSTANCES BY CHROMATOGRAPHY

METHODE POUR L'ANALYSE RAPIDE D'UN MELANGE DE SUBSTANCES PAR LA CHROMATOGRAPHIE

English Abstract

A METHOD FOR THE RAPID ANALYSIS
OF A MIXTURE OF A NUMBER OF
SUBSTANCES BY CHROMATOGRAPHY
Abstract of the Disclosure
In a first step, a chromatographic column is
calibrated by passing separately through the column each
constituent substance of the mixture to be analyzed and by
recording at the exit the pulse response of said substance.
In a second step, the mixture is passed through the column
and the total pulse response corresponding to the mixture
is recorded. In a third step, the concentration of each
substance is determined from the total pulse response
corresponding to the mixture and the specific pulse responses
of each substance.
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Claims

The embodiments of the invention in which an exclu-
sive property or privilege is claimed are defined as follows:
1. A method of chromatographic analysis of a mixture
consisting of more than two substances having specific signals
hi(t) wherein the chromatogram of said mixture is compared with
sample chromatograms of each of said substances to provide
percentages of the quantities of the different substances in
said mixture, comprising: passing each of said substances
through a chromatographic column having a length less than ten
centimeters and a retention time within a range of a few seconds
to two minutes, recording, at predetermined sampling instants
tj, values hj(tj) of the specific surface-normed response of
each substance i present in said mixture; measuring and
recording
(a) values x(tj), at said sampling instants tj, representing
the total surface-normed response of said mixture,
(b) values hj allowing to obtain the sum
hij = <IMG> hi(tk) hj(tk) of a matrix H having n columns, and
(c) values x allowing to obtain the sum bi = <IMG>
x(tj)hi(tj) of a matrix having one column by sum minimization of
S = <IMG> [x(tj) - <IMG> aihi(tj)]2 whereby elements hi-1j of the
inverse matrix of matrix H give values .alpha.1, where m is the
number of points sampled and .alpha.1 is the mass or molar percentages
of each of the n substances i in the mixture.

Description

1047791
This inventlon relates to a method for the rapld
analysis of a mixture of a number of substances by chromato-
graphy.
It is known that chromatographic analysis is a
highly efficient method for detecting and measuring the
components of a complex mixture of substances. However,
this method has the disadvantage of being time-consuming.
For example, in order to analyze a complex mixture of hydro-
carbons ranging from the paraffins to the aromatics, it is
thus necessary to employ a conventional chromatographic
column having a length of 3 to 10 meters and the time of
analysis is at least one half-hour.
This is highly objectionable when it proves
necessary for the operation of a refinery unit, for example,
to obtain rapid information at each instant in order to
permit automatic modification of column settings as a functlon
of the change in composition of the mixture. The conventional
chromatographic technique proves to be much too slow for thls
type of application and recourse must accordingly be had to
mass spectrometry but this process entails the use of cumber-
some equipment.
The present invention is precisely directed to a
method of rapid chromatographic analysis which overcomes the
disadvantages mentioned in the foregoing and makes it
possible in particular to obtain extremely rapid information
in regard to the composition of a mixture and to react and to
modify the settings automatically as a function of these
practically instantaneous data.
The method according to the invention lS charac-
terized in that, in a first step, a chromatographlc columnhaving a retention time withln the range of a few seconds to
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two mlnutes in the case of the most strongly retained
component is calibrated by passing separately through the
column each of the substances used for the formation of the
mixture which is to be subsequently analyzed in sald column
- and by recording at the exit the pulse response of each
substance aforesaid in respect of said column ; in a second
step, the mixture to be analyzed is passed through said column
and the total pulse response corresponding to said mixture is
recorded ; in a third step, the concentration of each sub-
stance aforesaid in the mixture is calculated by a suitable
mathematical method on the basis of the total pulse response
corresponding to the mixture and the specific pulse responses
of each substance. The retention time corresponding to the
retention time of the most strongly retained component is
therefore dependent on the number and nature of the sub-
stances to be separated. The minimum retention time in the
case of a simple separation process can be established at
approximately five seconds.
An advantageous feature of the method accordlng to
the invention lies in the fact that, in a first step and ln
the case of a given carrier gas flow velocity, each of the
substances used for the formation which is to be subsequently
analyzed is passed through the column, the specific pulse
response of each substance aforesaid is sampled as it is belng
recorded and the values hi(tj) of said response which lS
surface-normed are stored in memory at each sampling instant
tj ; in the second step, the mixture to be analyzed is passed
through the column, the total pulse response corresponding to
said mixture is sampled as it is being recorded and ~he values
x~tj) of said response are stored in memory at each sampling
instant t~ ; ln the thlrd step, the concentrat1on of each
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substance in the mixture is calculated by using the method of
least squares or in other words by minimizing the sum:
m n 1 2
S = ~ [x(tj) - ~ ~jh; (tj)J
where m is the number of sampled points and ~1 represents the
mass or molar percentages of each of the n substances i in the
mixture and there is then solved the system of n linear equations
having n unknown quantities ~j corresponding to the equation
aS/a~j = 0 in respect of each substance 1 from 1 to n.
A better understanding of the invention will be
obtained from the following description of one mode of execution
of the method according to the invention, reference being made
to the accompanying drawing in which:
Figure 1 is a block diagram of the device for carrying
out the method according to the present invention; and
Figure 2 shows a graph recorded by a plotter in the
case of a mixture used in one example of the method of the
present invention.
Use is made of a column having a short retention time
; of two minutes at a maximum and therefore a small length (10 to
20 cm) in respect of the usual carrier gas velocities.
Calibration of this column for each constituent of
the mixture to be analyzed is carried out as follows: each
substance is introduced separately into the chromatographic
column 1. At the exit of the column 1, the output signal corres-
ponding to said substànce is detected and passed into an
amplifier 2, then recorded in a plotter 3. At the same time,
the digital-analog converter 4 samples the signal and converts
the amplitude of each sample-to a numerical value which it
; stores on a support such as a disc 5, for example.
Thus in the case of each substance i of the mixture
which is subsequently to be analyzed, the pulse response
hj(t) is obtained and stored in memory.
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In order to carry out the analysis proper, the
mixture of n substances 1 whose specific signals hi(t) are
known is introduced into the column 1. The total pulse
response x(t) corresponding to this mixture is sampled and
recorded in the same manner as before.
Depending on the detector employed, the molar or
mass percentages of each substance in the mixture are ai :
n
~ a = 1.
i=l
The total surface-normed signal obtained from the
mixture is representative of the sum of signals of the n
components 1 of the mixture. We therefore have :
n
x(t) = aihi(t)
Since all the curves x(t) and hi~t) are surface- -
normed, it is necessary in order to determine the values
to minimize the sum :
m r n 2
S = ~ ¦x(t~ ihi (ti)l
j=l L i=l J
with respect to the values ~i. The values tj are the sampling
instants and _ represents the number of points of the total
signal x(t) sampled by the digital-analog converter 4.
In order to minimize, it is written that S is
stationary with respect to the percentages ~i' namely :
aS/aai = 0 in respect of each substance i from 1
to n, which gives n linear equations having n unknown
quantities ai, whlch are solved numerically by se~ting :
. . ~ .
. .
- . . : .
.
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1 ] 11
~ ~n L n ~
H is a matrix n.n corresponding to the general
term :
m
hij = hi (tk)hj (tk)
k=l
and
m
bi = x(tj)-hi(tj)
j=l
It is therefore apparent that the matrix H is
calculated once and for all in the case of a given group of
n substances 1 and in the case of a given carrier gas
velocity.
The computer 6 solves this system by means of the
data contained in the computer memory and the molar or mass
percentagss of each of the constituents of the mixture whlch
has thus been calculated are transmitted directly to the
typewriter 7.
By adopting the method according to the invention
and making use of a short chromatographic column having a
- short retention time, thus permitting a very rapid total
. pulse response which corresponds to the mixture and is too
imperfect to be read directly from the graph obtained but lS
processed mathematically by means of a computer equlpped wlth
` a digital-analog converter, a complex mixture of substances
can accordlngly be analyzed extremely rapidly. On the other
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hand,if conventlonal ehromatography is employed ln order to
obtaln the same result ln the form of a spectrum whlch repro-
duees the signals of eaeh eomponent with high resolutlon, the
length of time required would be at least ten times and in
many instanees up to fifty times as great.
Moreover, the method in aeeordance with the inven-
tion is advantageous from the point of view of quality of
information ; since the chromatographic analysis lS performed
very rapidly, this in fact circumvents the problems involved
in drift of the base line which is often encountered ln
chromatography.
Any type of chromatographic column can be employed
in the method according to the invention. However, lt lS
necessary to ensure that the amplitude of the signal obtained
in respect of a substance is proportional to the quantity of
said substanee introdueed into the eolumn and that the
prineiple of superposition ean be applied to the signal
obtained in the ease of a mixture ; it is therefore preferable
to operate with a low eoneentration and to avoid the use of a
gas-solid ehromatographie column.
When one of the substances assumed to be present
in the mixture is not present or has disappeared, an extremely
low or negative molar or mass percentage is obtained.
There is given hereunder a non-limitatlve example
of analysis of a mixture of hydrocarbons by means of the
method according to the invention.
Example :
It is sought to analyze a mixture of isopentane,
N-pentane, cyclopentane, hexane, ben~ene, cyc~ohexane,
cyclohexene, heptane and methylcyelohexane~
A Perkln-Elmer F-20 ehromatographlc column of the

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flame ionlzation type ls employed. The column has a length
of 15 cm, a diameter of approximately 0.3 cm and is brought
to a fixed temperature within the range of 70 to 120C. The
stationary phase is constituted by squalane on "chromosorb"
and the carrier gas consists of helium.
When the different constltuents aforesaid have
been introduced successively into the column in respect of a
carrler gas velocity of 20 cm3 per minute, and when the results
obtained in respect of each of these substances have been
stored in memory, the mixture is introduced and the total
result obtained is recorded.
The computer performs the calculation described
earlier and transmits this latter to the typewriter whlch
directly gives the molar or mass percentages of the dlfferent
substances in the mixture. The following table gives these
results.
Substance Percentage
A = Isopentane :5 %
B = N-pentane :2 %
C = Cyclopentane :14 %
D = Hexane :21 %
E = Benzene :12 %
F = Cyclohexane :21 %
G = Cyclohexene :4 %
H = Heptane :11 %
I = Methylcyclohexane :7 %
The degree of accuracy achieved ln the results
obtalned is of the order of 5 %.
t The accompanylng figure 2 shows the graph whlch lS
recorded by the plotter in the case of said mlxture ln a
period of ten seconds. The ful~-line curve represents t~e
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graph whlch corresponds to the mlxture. By way of a check,
s ~lhl ' ~2h2 ~ ~3h3 etc- which correspond to the
identification signals of each constituent of the mixture
have been plotted in dashed lines.
The analysis of this mixture was carried out ln a
time interval of approximately 30 seconds (10 seconds of
analysis and 20 seconds of calculation in an IBM 1800 computer
having a basic cycle of 2~s). It is therefore apparent that
the method according to the invention permlts extremely rapld
determination of the presence and concentration of components
in a mixture.
The method according to the invention is appl1cable
to any industrial method of conversion in which recourse lS
had to chromatographic analyses.